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<H1>Greedy Sparse Signal Recovery</H1>


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  <LI><A title=Introduction  href="#intro"><STRONG>Introduction</STRONG></A>
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<H2><A id=intro name=Introduction></A>Introduction</H2>

<H3>1、ECME Thresholding Pursuits</H3>

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<P>
<P><STRONG>Abstract:</STRONG></P>
Recent years have witnessed increasing interest in sparse signal processing. The emerging theory of compressive
sensing provides a new sparse signal processing paradigm for reconstructing sparse signals from the
undersampled linear measurements. In this paper, we developed two approaches for finding sparse solutions to
underdetermined inverse problem in compressed sensing. The described algorithms, named ECME thresholding
pursuits (EMTP), introduced two greedy strategies that each iteration detects a support set I by thresholding
the result of the ECME iteration and estimates the reconstructed signal by solving a truncated least-squares
problem on the support set I. Two effective support detection strategies (hard thresholding and dynamic
thresholding) are devised for the sparse signals with components having a fast decaying distribution of nonzero
components. The hard thresholding iteratively maintains k largest nonzeros in magnitude of the ECME
iteration. The dynamic thresholding iteratively selects nonzero elements greater than an exponentially
decreasing threshold. The experimental studies are presented to demonstrate that EMTP offers an attractive
alternative to state-of-the-art algorithms for sparse signal recovery.
</P>

<P><STRONG>Demo</STRONG></P>
<P class=image>
<IMG alt="" src="paper/EMTP01.png" height="60%">
</P>
<P class=image>
<IMG alt="" src="paper/EMTP02.png" height="60%">
</P>
<P class=image>
<IMG alt="" src="paper/EMTP03.png" height="60%">
</P>
<P class=image>
<IMG alt="" src="paper/EMTP04.png" height="60%">
</P>
<P><STRONG>EMTP with hard thresholding</STRONG></P>

<H3>1、IDE</H3>

<P><A href="#top">TOP</A></P>

<H2><A id=Papers  name=Papers></A>Papers</H2>
<OL>

        <LI>                
        <STRONG>Heping Song</STRONG> and Guoli Wang.
         <EM>
         Sparse Signal Recovery via ECME Thresholding Pursuits.
         </EM>
        Mathematical Problems in Engineering, Volume 2012 (2012), Article ID 478931, 22 pages.
	[<A href="http://dx.doi.org/10.1155/2012/478931" target="_blank">DOI</A>]
        [<A href="./paper/mpe12.pdf" target="_blank">pdf</A>]
         </LI>


</OL>
<P><A href="#top">TOP</A></P>

<H2><A id=Download name=Download></A>Download</H2>
<OL>
        <LI>Code for <EM>EMTP</EM>. <A  href="./paper/EMTP.7z">Download</A>
        <LI>Slides for <EM>Greedy Sparse Signal Recovery</EM>. <A href="./paper/GSSR_ppt.pdf">Download</A> </LI>

</OL>


<P><A href="#top">TOP</A></P>

<H2><A id=Links name=Links></A>Related Links</H2>
<ul>
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<li>YALL1 [<a href="  ">link</a>]</li>
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  <UL>
        <li>DORE -- Double overrelaxation thresholding  [<a href="http://home.engineering.iastate.edu/~kqiu/DOREpage/DORE.htm">link</a>]</li>
        <li>ISD -- Iterative Support Detection  [<a href="http://www.caam.rice.edu/~optimization/L1/ISD/">link</a>]</li>
        </li><li>l1_magic [<a href="http://www.acm.caltech.edu/l1magic/">link</a>]</li>
        <li>SparseLab [<a href="http://sparselab.stanford.edu/">link</a>]</li>
        <li>Bregman Iterative l1-Regularization [<a href="http://www.caam.rice.edu/%7Eoptimization/L1/2006/10/bregman-iterative-algorithms-for.html">link</a>]</li>
        <li>YALL1 [<a href="http://www.caam.rice.edu/%7Eoptimization/L1/YALL1/">link</a>]</li>
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    <TD align=middle><SPAN class=footdate>Updated: 2011-7-15</SPAN> </TD>
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